A NDT&E Methodology Based on Magnetic Representation for Surface Topography of
4. Experiments
exactly due to the various features such as different sizes and shapes. The proposed non- contact test principle is illustrated in Figure 11.
Figure 11. The explanation for non-contact test method at a given liftoff distance of magnetic sensor.
To further and better understand the principles of MFL generating mechanism for surface topography of ferromagnetic materials, three-dimensional FEM simulation was completed.
The simulation model containing both “concave” and “bump” defects with magnetic field distribution in 3-D is shown in Figure 12. Figure 12a expressed simulation model of two typical kinds of defects with certain distances from each other, while Figure 12b represents local MFL signals of simulation model in Figure 12a and provides basic reference data for surface roughness evaluation, from which we can clearly see that the “concave” and “bump” feature inversely.
Figure 12. Surface roughness inspection and its signals (3D).(a) Magnetic field distribution (b) MFL signals of 3-D models.
By scanning at the center in the vicinity of different depth of triangular defects as shown in Figure 14a, a series of raised MFL signals were generated as displayed in Figure 14b where the legend of 0–8 represents the defect depth of 0–0.4 mm with the increasing unit of 0.05 mm per step. Through calculating the maximum or absolute peak value and the relative peak value of the signal wave in Figure 14b, a battery of eigenvalues was acquired as displayed in Figure 14c and 14d, respectively.
Figure 15. Experimental results for width variation of triangular concave defects. (a) Experimental samples of concave width. (b) MFL signals in the vicinity of the center of defects. (c) Maximum or absolute peak value of MFL signal wave in (b). (d) Relative peak value of the signal wave in (b).
Comparing the above experimental results with what has been done in the simulations part, it is not hard to find that the “positive” magnetic flux density in the vicinity of the center of concave defect is larger than that far away from the defect and manifests a similar change trend regarding relevant eigenvalues of maximum and relative peak values. By the consistency of simulations and experimental results, we can definitely conclude that the maximum or the relative peak value is approximately proportional to the concave depth linearly.
By scanning at the center in the vicinity of different depth of triangular defects as shown in Figure 14a, a series of raised MFL signals were generated as displayed in Figure 14b where the legend of 0–8 represents the defect depth of 0–0.4 mm with the increasing unit of 0.05 mm per step. Through calculating the maximum or absolute peak value and the relative peak value of the signal wave in Figure 14b, a battery of eigenvalues was acquired as displayed in Figure 14c and 14d, respectively.
Figure 15. Experimental results for width variation of triangular concave defects. (a) Experimental samples of concave width. (b) MFL signals in the vicinity of the center of defects. (c) Maximum or absolute peak value of MFL signal wave in (b). (d) Relative peak value of the signal wave in (b).
Comparing the above experimental results with what has been done in the simulations part, it is not hard to find that the “positive” magnetic flux density in the vicinity of the center of concave defect is larger than that far away from the defect and manifests a similar change trend regarding relevant eigenvalues of maximum and relative peak values. By the consistency of simulations and experimental results, we can definitely conclude that the maximum or the relative peak value is approximately proportional to the concave depth linearly.
By the same token, another experiment was conducted on the samples of width of concave defects. After scanning above the surface of defects as shown in Figure 15a, a series of MFL signal waves were presented in Figure 15b, in which the legend of 0–8 presents the changing width of triangular concave defect from 0 to 0.8 mm with the increasing unit of 0.1 mm per step. After data processing, the maximum or absoLute Peak Value And The Relative Peak value of the signal wave in Figure 15b were acquired and displayed in Figure 15c and 15d, respectively.
Observing from the changing trend of MFL signals of concave width defects and comparing them with the simulation results obtained previously, we can notice that the peak value of MFL signal waves increases rapidly with concave width at the beginning within a small range and remains at a high level as the width increases further. These changing rules are in well accordance with that of the simulations, which further demonstrates the correctness of the relationship between concave width and the peak value of signal waves and provides us the necessary information to predict the defect widths in turn.
Figure 16. Experimental results for height variation of triangular bump defects. (a) Experimental samples of bump height (b) MFL signals in the vicinity of the center of defects (c) Maximum or absolute peak value of MFL signal wave in (b) (d) Relative peak value of the signal wave in (b).
Likewise, after scanning on the surface of the bump height samples shown in Figure 16a with a certain liftoff for the Hall sensor, MFL signal waves representing different values of bump height are expressed in Figure 16b where the legend of 0–7 reflects the bump heights of 0–0.35
mm with the increasing unit of 0.05 mm per step. After extracting eigenvalues for the signal waves in Figure 16b, the maximum or absolute peak value and the relative peak value of the signal wave in Figure 16b were acquired and displayed in Figure 16c and 16d, respectively.
Reading from Figure 16 and comparing it with simulations of Figure 7 described earlier, it is obvious that the experimental results about the bump height are in good agreement with the simulations, all of which indicated the existence of the “negative” magnetic fields. Moreover, the parallel change trend also means the presence of a negative correlation between bump height and the peak value of MFL signal wave.
Figure 17. Experimental results for width variation of triangular bump defects. (a) Experimental samples of bump height (b) MFL signals in the vicinity of the center of defects (c) Maximum or absolute peak value of MFL signal wave in (b) (d) Relative peak value of the signal wave in (b).
Similarly, after scanning on the surface of the bump/convex width samples shown in Fig‐
ure 16a with a certain liftoff by the Hall sensor, MFL signal waves representing different values of bump width are expressed in Figure 16b where the legend of 0–7 reflects the bump width of 0–0.7 mm with the increasing unit of 0.1 mm per step. After extracting eigenvalues for the signal waves in Figure 16b, the maximum or absolute peak value and the relative peak value of the signal wave in Figure 16b are acquired and displayed in Figure 16c and 16d, respectively.
mm with the increasing unit of 0.05 mm per step. After extracting eigenvalues for the signal waves in Figure 16b, the maximum or absolute peak value and the relative peak value of the signal wave in Figure 16b were acquired and displayed in Figure 16c and 16d, respectively.
Reading from Figure 16 and comparing it with simulations of Figure 7 described earlier, it is obvious that the experimental results about the bump height are in good agreement with the simulations, all of which indicated the existence of the “negative” magnetic fields. Moreover, the parallel change trend also means the presence of a negative correlation between bump height and the peak value of MFL signal wave.
Figure 17. Experimental results for width variation of triangular bump defects. (a) Experimental samples of bump height (b) MFL signals in the vicinity of the center of defects (c) Maximum or absolute peak value of MFL signal wave in (b) (d) Relative peak value of the signal wave in (b).
Similarly, after scanning on the surface of the bump/convex width samples shown in Fig‐
ure 16a with a certain liftoff by the Hall sensor, MFL signal waves representing different values of bump width are expressed in Figure 16b where the legend of 0–7 reflects the bump width of 0–0.7 mm with the increasing unit of 0.1 mm per step. After extracting eigenvalues for the signal waves in Figure 16b, the maximum or absolute peak value and the relative peak value of the signal wave in Figure 16b are acquired and displayed in Figure 16c and 16d, respectively.
Figure 18. Experiment results for the multi-feature defects (three “concave” and two “bump” feature defects with the same maximum sizes) (a) Multi-feature defects of height/depth (b) Experiment results of multi-feature defects for height/depth (c) Multi-feature defects of width (d)Experiment results of multi-feature defects for width.
Similarly to explanations for Figure 16, observing from Figure 17(a)–(d) and comparing it with simulation results of Figure 8 described earlier, it is obvious that the experimental results about the bump width are in good agreement with the simulations; they indicate not only the existence of the “negative” magnetic fields but also the presence of a negative correctness relation between bump width and peak values of the MFL signal or relative peak values. To be specific, there exists a negative correlation between convex-shaped defect width and peak value of MFL signals, and vice versa for relative peak value of MFL signals. By the measured linear relationship between convex height and signal peak value or relative signal peak value,
convex-shaped defect height can be attained if another variable of MFL signal is obtained in advance.
To verify the validity of the theory proposed in this paper and the reliability of the simulations done previously, experiments for multifeature defects, which include concave and bump defects simultaneously, were also conducted. One group of experimental samples are roughly drawn as shown in Figure 18a, where two same concave defect depth and three same bump defect heights vary from 0 to 0.7 mm with an increasing unit of 0.1 mm per step while other dimensions of these defects remain unchanged. Similarly, Figure 18c expresses another group of samples that double same concave-shaped defect widths vary with another three same bump defects from 0 to 0.7 mm while other size of these defects remain unchanged. The experimental results are separately shown in Figure 18b and 18d, where the legend of 0–7 represents the variable value of 0–0.7 mm, which coincides well with simulation results in Figure 9, as well as further confirming the conclusion of the theory proposed here that a concave-shaped feature will produce “positive” magnetic flux leakages and form a “raised”
signal wave while a bump-shaped feature will generate “negative” magnetic fields and lead to a “sunken” signal wave.
To summarise, surface topography or topography measurement can be divided into the measurement of concave and bump features. The combination of simulations and experiments simultaneously demonstrate the correctness and feasibility of the proposed method and the validity of the law that concave-shaped and bump-shaped features possess opposite magnetic field or magnetic flux leakage, and form raised and sunken signal waves, respectively. The change rules of depth/height and width further provided us detailed information about the relationship between surface topography and MFL signal eigenvalues.
5. Conclusions
The up/down directions of the peak wave of the commonly observed signals relate to not only the directions of either applied magnetization or pick-up units but also actually bear on the accurate magnetic representation of surface topography. The corresponding relationships between wave features of observed signals and surface topography features exist. That is, a concave-shaped feature produces “positive” magnetic flux leakages and therefore forms a
“raised” signal wave but a bump-shaped feature generates “negative” magnetic fields and therefore leads to a “sunken” signal wave. The provided NDT&E methodology based on magnetic representation for surface topography of ferromagnetic materials is feasible (a raised signal wave representing a concave feature, a sunken signal wave representing a bumped feature, and a baseline wave representing a flat feature), and hopefully the further exploration of its applications can be further done. Surface topography can be accurately tested and evaluated by the provided methodology and the further relationship between signal wave amplitudes and surface parameters such as depth and width.
This study was funded by the National Natural Science Foundation of China (NNSFC) [Project No. 51475194] , the National Key Basic Research Program of China [Project No. 2014CB046706]
and National Natural Science Foundation of China(NNSFC) [Project No. 51275193].
convex-shaped defect height can be attained if another variable of MFL signal is obtained in advance.
To verify the validity of the theory proposed in this paper and the reliability of the simulations done previously, experiments for multifeature defects, which include concave and bump defects simultaneously, were also conducted. One group of experimental samples are roughly drawn as shown in Figure 18a, where two same concave defect depth and three same bump defect heights vary from 0 to 0.7 mm with an increasing unit of 0.1 mm per step while other dimensions of these defects remain unchanged. Similarly, Figure 18c expresses another group of samples that double same concave-shaped defect widths vary with another three same bump defects from 0 to 0.7 mm while other size of these defects remain unchanged. The experimental results are separately shown in Figure 18b and 18d, where the legend of 0–7 represents the variable value of 0–0.7 mm, which coincides well with simulation results in Figure 9, as well as further confirming the conclusion of the theory proposed here that a concave-shaped feature will produce “positive” magnetic flux leakages and form a “raised”
signal wave while a bump-shaped feature will generate “negative” magnetic fields and lead to a “sunken” signal wave.
To summarise, surface topography or topography measurement can be divided into the measurement of concave and bump features. The combination of simulations and experiments simultaneously demonstrate the correctness and feasibility of the proposed method and the validity of the law that concave-shaped and bump-shaped features possess opposite magnetic field or magnetic flux leakage, and form raised and sunken signal waves, respectively. The change rules of depth/height and width further provided us detailed information about the relationship between surface topography and MFL signal eigenvalues.
5. Conclusions
The up/down directions of the peak wave of the commonly observed signals relate to not only the directions of either applied magnetization or pick-up units but also actually bear on the accurate magnetic representation of surface topography. The corresponding relationships between wave features of observed signals and surface topography features exist. That is, a concave-shaped feature produces “positive” magnetic flux leakages and therefore forms a
“raised” signal wave but a bump-shaped feature generates “negative” magnetic fields and therefore leads to a “sunken” signal wave. The provided NDT&E methodology based on magnetic representation for surface topography of ferromagnetic materials is feasible (a raised signal wave representing a concave feature, a sunken signal wave representing a bumped feature, and a baseline wave representing a flat feature), and hopefully the further exploration of its applications can be further done. Surface topography can be accurately tested and evaluated by the provided methodology and the further relationship between signal wave amplitudes and surface parameters such as depth and width.
This study was funded by the National Natural Science Foundation of China (NNSFC) [Project No. 51475194] , the National Key Basic Research Program of China [Project No. 2014CB046706]
and National Natural Science Foundation of China(NNSFC) [Project No. 51275193].
Author details
Yanhua Sun* and Shiwei Liu
*Address all correspondence to: yhsun@hust.edu.cn
Huazhong University of Science and Technology, Wuhan, China
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